To understand both the spectral discrimination and the image production from an imaging spectrometer requires both Gaussian, or geometrical, and physical optics that govern the processes of diffraction and interference. This appendix provides the barest introduction to Gaussian optics and a qualitative description of aberration theory. Physical optics is introduced in Chapter 4 when it is required, as in, for example, the action of a grating. The analysis presented is for centered or axially symmetric systems about an axis that passes through the centers of the sequential optical elements known as the optical axis. The concept of paraxial ray tracing, where the rays travel infinitesimally close to the optical axis, is also introduced, providing the location and size of the image. The brightness of an image is developed through the definition and placement of pupils and stops. Finally the quality of an image is determined through aberration theory.

The Optical Path

In Chapter 2 we introduced the concept of a wavefront as the surface of constant phase for an electromagnetic wave. This surface is perpendicular to the wave vector k, which is in the direction of propagation of the wave. A ray of light is defined to be parallel to the wave vector and is in the direction of energy propagation as described by the Poynting vector. The ray, an infinitely narrow beam of light, is the construct used in geometrical optics but has no precise physical meaning. For example, if we attempt to create a narrow beam of light by illuminating a pinhole we are defeated by diffraction effects that spread the beam out, with the effect becoming larger as the pinhole diameter is reduced. Nevertheless the ray is an extremely useful and practical concept that is universally used in Gaussian optics and ray tracing. The wavefront, on the other hand, has a precise physical meaning and, for the isotropic materials used in imaging spectrometers, the direction of energy propagation is always along the wavefront normal.

In Gaussian optics, light is assumed to propagate rectilinearly along the rays with their directions changed only by the processes of reflection and refraction. The optical systems considered here are composed of a series of surfaces that can be either refracting or reflecting and have a common axis of rotational symmetry known as the optical axis.